Deep Learning is more than a pack of techniques showing improving performance updating on benchmarks. I will focus on mathematics related to the comprehensive developments of the deep neural network (DNN). I plan to cover as many more topics on AI explanation, together with at least Generative AIs (GAN, VAE, and diffusion models), Generalization error analysis (PAC, Rademacher, and VC-dimension), Ranking by Sharpley values (Game), and but not the least Kenel machines (NTKs).

Compared to the model-based approach, where a problem typically summarizes the domain knowledge into a low-dimension optimization problem under a priori constraints, the breakthrough of the data-driven approach is a full-of-future, new field to young mathematicians. This course can inspire students to develop new analytical techniques on this emerging topic.

Basic knowledge of engineering aspect of Deep NNs.

Dependent on how hungry a student is.

Written in my notes.

Written in my class notes